GWEN IFILL: Saudi Arabia abruptly announced an end today to a month-long air campaign against Shiite rebels in Yemen. The Saudis and their Sunni allies said they will focus on political efforts, but continue military action as needed.

At the same time, a senior rebel leader said a political accord is almost ready.

Meanwhile, the White House explained its decision to send in the aircraft carrier Theodore Roosevelt.

JOSH EARNEST, White House Press Secretary: The movement of the — of this particular aircraft carrier would augment the American military presence in the Gulf of Aden, and would send a clear signal about our continued insistence about the free flow of commerce and the freedom of movement in the region.

GWEN IFILL: That effort could also include intercepting Iranian vessels trying to ferry weapons to the rebels.

For more on all this, we turn now to our chief foreign affairs correspondent, Margaret Warner.

Margaret, what was behind Saudi Arabia's decision to suspend whatever it is they were doing, their military action?

MARGARET WARNER: Gwen, U.S. officials believe that it was basically a cost-benefit analysis by the Saudis, that in fact the costs were outweighing the benefits.

That is, this has been going on a month. They have been heavily criticized internationally for a lot of civilian deaths. They have not achieved two of their three main objectives, which was to roll the Houthis back north. That didn't work upon. And to restore the President Hadi to power, which they have not been able to do, and that that was going to require a ground campaign, which they don't have the assets to do despite what they spend on military hardware, and no one was willing to help them, including the Pakistanis.

Secondly, and very importantly, the U.S. was really pressing them hard. The U.S. was concerned about all the civilian casualties. The U.S. intelligence view is, they had an objective, but they never really had a plan. They never thought through how to do it. And the U.S. was very, very concerned that all this chaos is giving al-Qaida in the Arabian Peninsula and other really extremist terrorist groups more room to operate.

And a senior intelligence person told me today that in fact AQAP operations have increased in this month. So, from a U.S. perspective, it was time to roll this back, freeze this in place, and try to get a political dialogue going.

GWEN IFILL: You said that Saudi Arabia didn't achieve its goal of rolling back the Houthis. Yet they announced this afternoon that they are going to also step back, that some sort of accord has been reached?

MARGARET WARNER: Well, there is. And I have just confirmed this with both U.S. officials and people close to the Saudis.

There is a commitment on the part of both the Houthis and the Saudis to get back to some sort of political dialogue, which originally was under the umbrella of the U.N. and the Gulf Cooperation Council and so on. Now, U.S. officials think it's for real, though they are very cautious about this.

But, apparently, a White House statement is about to come out applauding the Saudi decision and saying — applauding the chances for political dialogue, and, most important, talking about the possibility of resuming humanitarian aid.

GWEN IFILL: You're always ahead of the curve on these things, Margaret, but I want to ask you about one more thing, and that is Iran's role in all of this. They always seem to be in the middle of every conflict.

MARGARET WARNER: And they are indeed, Gwen.

Do you know that it was this morning that the Iranians put out a little notice statement in which they predicted the Saudis were about to suspend their air campaign? This is hours before the Saudis did it. So they knew something everybody else didn't know.

Secondly — and I don't know if we can say that they have been encouraging the Houthis to go to political dialogue. Certainly, the U.S. has been working the Saudis hard. I'm prepared and I could not confirm that there has been any kind of tacit or whatever communication here because, obviously, also, the U.S. is being very critical of Iran for moving ships in the area and are they moving weapons and so on.

And, of course, this all gets tangled up with the Iranian nuclear talks. And part of reason the U.S. got sucked into this in the first place, if you look at the timing, March 26, this was just as they were neither a deal with Iran and they wanted to assure their Gulf partners that, no, no, the U.S. isn't abandoning them.

You can figure Iran is playing a major role here, both overtly and as a sort of, yes, motivation.

GWEN IFILL: It is a tangled web, as always.

MARGARET WARNER: As always.

GWEN IFILL: Margaret Warner, thank you.

MARGARET WARNER: Always a pleasure.